Identifier

etd-0409103-153131

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are determined. Some conditions are also given for when the moduli spaces are connected and when they are disjoint unions of two moduli spaces of polygonal linkages.

Date

2003

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

J. William Hoffman

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